There is known a drive system for a hybrid vehicle, which is provided with an engine, an electric motor, a clutch disposed in a power transmitting path between the engine and the electric motor, and a transmission of a step-variable type disposed in a power transmitting path between the electric motor and drive wheels. In the field of such type of hybrid vehicle drive system, there has been proposed a technique to improve an acceleration response to an operation of an accelerator pedal. For example, Patent Document 1 discloses a method of starting the engine of the hybrid vehicle drive system.